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Tear Jerker: Valvrave the Liberator
Episode 1: Shoko's apparent death. Even after avenging her and earning the respect and admiration of all of his peers in the process, Haruto still breaks down into tears once the battle is over.
L-Elf's near-murder of Haruto is rather heart-wrenching. After beating the odds and surviving in a nearly impossible situation, we go from cheering high school students, to seeing poor Haruto, who in no way has had an easy day getting stabbed through the heart and shot in the chest. Thankfully, it doesn't stick.
It's only worse when you realize that L-Elf's words to Haruto earlier in the episode played a key role in his mustering up the courage to win the battle.
Episode 2: Haruto stopping himself from confessing to Shoko because that he feels that what the Valvrave has done to him means that he is a monster, and monsters aren't supposed to have feelings.
The translation is a bit suspect on that one. Haruto simply says that he doesn't have a right to convey his feelings to her, not that he has none.
In Episode 5, during the video the Sakimori students produce to boost Jioran morale and raise funds, you can see a girl holding a photo—likely of a loved one who died in the attack.
Episode 7: Aina's death. She was in the wrong place at the wrong time and Q-Vier disobeyed a direct order to capture them, instead shooting to kill.
To elaborate, she'd been holding onto hope that her father, the Prime Minister of Jior had gotten away from the Dorsians, only to find that they'd captured him and are now using him as a bargaining chip. She's told to choose between letting him die or handing over the Valvraves and getting freedom for him, her friends and all of their families, and the chance to evacuate to another country without retaliation in exchange—but with the added cost of abandoning the rest of the Jioran people. Her father then ignores his captors' aggressive attempts to shut him up by saying that he's incredibly proud of Shoko, and that her destiny is in her future, not her past. Once the Dorsian fleet is wiped out and he disappears along with it, cutting off the video feed Shoko understandably breaks down crying.
Episode 16. Marie's battle.
Episode 19. Lieselotte's death, and L-Elf's reaction to seeing her corpse flying through the air.